Correct me if I'm wrong, but observations do show there's a significant problem with the equations, which led to the invention of "dark matter" and "dark energy".
Aside from that, is there any connection between the universal constants of physics and mathematical constants? It would be nice to be able to say, "The Universe is the way it is because circles."
When the scientific consensus reached a point where it was agreed on that the universe is accelerating the cosmological constant came back into play because with it you can explain the accelerated expansion, the problem is that we can't account for the additional energy needed to account for the acceleration so dark energy was introduced as a concept.
Dark Matter was introduced to solve another issue, one that can be seen on much smaller (or own galaxy) scales, basically if we look at the motion of stars and the rotation of galaxies we seem to be lacking mass, and quite a bit of it (although not nearly as much as dark energy) so again a place holder device was introduced in the form of dark matter
Now normally you would say well when you need to introduce additional doodads to account for something in your theory not in 1 instance but in 2 and maybe in many others your theory sucks. The problem is that we've sorta proven that gravity works for the most part as we think it does, and if we go into weird stuff like localized gravitational constants well they don't account for the observations that required dark matter or energy, oh and they kinda break the universe.
The force of gravity and hence the gravitational constant has been proven to be "correct" in from the smallest (even atom level) observations and calculations to the macro and universal scales, and while it's true that we might be wrong, if we are we are wrong by not a mile but probably several parsecs this means that relativity and other current accepted gravitational theories are more wrong than the "Ether Theory".
They are locally correct, just like Newton's theories were correct up until we observed Mercury.
That being said I'm 99% in agreement with mainstream science: Einstein's work just makes too much sense to be wholly incorrect. Where I'm in strong disagreement with mainstream science is outright hacks where they turn dark matter/energy into real things (e.g. WIMPs). Non-constant G is a more worthwhile avenue than that IMO.
> MOND
I'm not saying that MOND is correct at all, I'm saying that we believed that classical Newtonian dynamics was seen as correct at one point - just like SR is seen as correct now. My opinion is that it's highly unlikely that SR is incorrect (or partially incorrect), however, I do see it as a remote possibility.
> There are filaments and voids where the gravitational effects of unseen matter/stuff are plainly observable
Another way of looking at it is a map of the sum of things that we don't know. Again, using Mercury as an example, we were able to calculate the [sum of] force the was "wrong." The dark matter map is incredibly cool because it's the same thing done on a unbelievably massive scale. There were certainly people who believed that this unaccounted-for force on Mercury was a single force with a trivial explanation. We now know that this was not the case.
That is, in my opinion, the same mistake we are now making - simply because we can calculate a map of the effect does not mean that it's actually a map of real stuff.
Although I'm in disagreement with MOND I do think it does something right: the μ function. "This is something that we don't know." In the same way it is in my opinion that dark matter and dark energy are merely unknown functions and not "real matter" and "real energy." I certainly think that Turner and Zwicky had the same thought pattern when they coined the terms.
Sadly Jacob Bekenstein died just a month ago and I'm not sure how much work will be done on MOND now.
Non-Constant G just breaks the universe, it's also not exactly "Non-Constant" it's still constant just at a different value as far as dark energy goes. But considering that we calculate the value correctly on a local scale it makes very little sense that is changes all of a sudden especially considering that it changes the same everywhere including within our galaxy.
Dark matter is there to fix another very different picture because without it you'll have an almost completely random gravitational constant even on small scales - star systems, and galaxies, this simply can't be the case. Even without going into relativity if you have a classical system (stars) that doesn't account for the motion you are missing mass some where.
Now there are other attempts to explain some of these effects e.g. the gravitational waves from super massive black holes that are slamming into each other, new experiments predominately those which will measure pulsars are will attempt to discover and measure those with much greater accuracy which might account for some of the randomness but won't account for the fact that we need more mass and energy in the universe to make things work.
Science has always used placeholders and mechanisms for things that should be there but weren't discovered, this is the great thing of good science because it's predictive, and more often than not it works, even when you don't understand the entire picture.
A great example of this is the periodic table it was constructed by pure observation of the attributes of various elements, it predated the standard model, the discovery of protons, neutrons, isotopes and the such. However it was so correct that it didn't matter because the principle worked and the extrapolated attributes of the elements were enough to build a system that didn't had to be changed when you figured out how all the internal gadgets work.
Now the Precession of Mercury is actually a great example, Newtonian laws of motion account for just under 95% of Mercury's orbital velocity, relativity (the fact that mass curves space) accounts for the missing 5%. Before we understood relativity we had planet Vulcan which was the doodad that science constructed to explain the orbital mechanics of Mercury.
The big difference between Mercury and Dark Matter/Energy is that we need to find something that works on all scales, the need for dark matter and dark energy comes from relative small scales as well as very big ones, now there could be some other force or phenomenon we completely don't understand but you also can't look for something completely unknown. You would be hard pressed to look at something like the orbit of mercury and come up with relativity as an explanation that just wont work, you'll never end up with that as a result. Dark Matter or Dark Energy for the other hand are much wider place holders than a Planet X.
On top of that Dark Matter is not only needed to explain relativity but is also predicted by other theories mainly big bang nucleosynthesis, it may also be needed (or could account for) various observations of gravitational microlensing since MACHO's don't seem to be able to account for all of those.
And as far as WIMP's go well they aren't hacks, these are predicted by quite a few of nucleosynthesis theories that go beyond the standard model, we already have weak interactive particles, but they all tend to be extremely light however mass doesn't seem to play a role in their nature so WIMP's could very well exists, people didn't think neutrino's were real either.
> Now there are other attempts to explain some of these effects e.g. the gravitational waves from super massive black holes [...]
We just need to be looking at other options. It seems as though we are spending a lot of thinking time on one solution and it's frustration with that which likely leads me to words such as "hacks."
> Mercury
I wasn't suggesting it was the same thing, merely making an analogy: a somewhat similar type of mistake we made in the past. WIMPs could be real but they could just be the modern day Vulcan: I watched a great talk by Prof. Terry Rudolph[1] and he points out that our monkey brains have problems visualizing things smaller than "banana." Possibly our brains have problem visualizing forces bigger than "moon" and therefore we create these physical phenomena (Vulcan/WIMP) in a desperate attempt to conceptualize them.
While WIMPs may very well be the correct solution, I'd just like to see a little more energy spent exploring other solutions. Science is very much about being correct nowadays: getting published, getting the Nobel Prize, etc. I think it's far more rewarding to be wrong and science needs to briefly contemplate the philosophical roots that it was born of.
But we are looking, both dark matter and dark energy have multiple candidates.
Maybe Einstein was correct and we have a (small but positive) universal constant AKA space-time's property tax. Other various proposed fields like the quintessence theory, and some various views on QFT could also be an answer to that.
So you have allot of different theories and proposal from small hacks like the universal constant to completely new theories but they pretty much are aimed and answering the same thing and are labeled under "dark energy".
Dark matter is the same thing, most candidates for dark matter are quite different and they all attempt to explain why we are all fatter than we think we are through different mechanisms.
We also have some other efforts to create completely different explanations for gravity like MOND that was mentioned.
So I don't really see that we are limiting ourselves, but as I said before you have to start searching for something at a known point or go completely out of left field, and so far usually you need a little (or well allot) of both because rarely (at least these days) were we can be off by so much that we need to rewrite the text books.